The principal tools in LR theory, viz. item grammars and their corresponding automata, are adapted for use with affix grammars. The items (and automata states) are furnished with attributes that serve as pointers into the parsing stack and thus determine the inherited affixes needed in a reduction step. This attribute mechanism can be tested for ambiguity. If unambiguous and consistent in the sense of LR theory, the attributed automaton defines a deterministec bottom-up parser for the affix grammar in question.